Spectra and Pgas for the Assessment and Reconstruction of Christchurch

G.H. McVerry, M.C. Gerstenberger, D.A. Rhoades & M.W. Stirling GNS Science, Lower Hutt, New Zealand.

2012 NZSEE Conference ABSTRACT: Spectra and peak ground accelerations for the assessment and rebuilding of structures in Christchurch were revised rapidly following the magnitude 6.2 earthquake on 22 February 2011. The NZS1170.5:2004 hazard factor Z for Christchurch was quickly raised from 0.22 to 0.3. There have been different requirements for different purposes: spectra for the design of new structures and the assessment of existing ones, and peak ground accelerations for liquefaction assessments and for evaluating the probabilities of rock falls in the Port Hills. Particularly challenging has been the need to take into account the time-varying nature of a productive on-going earthquake sequence. The increased design levels recognise that the motions in Christchurch were abnormally strong, the strongest that have been recorded in any New Zealand earthquake. Ground motions around the CBD were enhanced by factors of about 2 or more from median values given by local and US ground- motion prediction equations for the magnitude and distance of the earthquake. The recorded CBD motions were generally about double the 500-year design motions for Christchurch. Systematic effects such as enhanced stress-drop, rupture-directivity, site-effects and basin effects are being modelled.

1 INTRODUCTION

The seismic sequence initiated by the magnitude 7.1 Darfield earthquake of 4 September 2010 has increased the seismic hazard in the Christchurch region. This increase is likely to persist, although gradually reducing, for several decades. The motions experienced in the Christchurch Central Business District (CBD) in the magnitude 6.3 earthquake of 22 February 2011 were considerably greater than design motions specified in the New Zealand structural design standard NZS1170.5:2004 (Standards New Zealand, 2004). The recorded motions in the CBD were enhanced by factors of about 2 from median values given by both New Zealand and US ground-motion prediction equations (see Section 1.1). The peak accelerations in this earthquake were the strongest recorded in New Zealand, with maximum values of 2.2g vertically and 1.7g horizontally, with over 0.7g horizontally around the CBD. These factors led to a preliminary reassessment of the hazard factor Z and the associated return period factors R of the NZS1170.5:2004 design standard and the assessment of peak ground accele rations for liquefaction assessment soon after the 22 February earthquake, using time-varying seismic source models to represent the on-going earthquake sequence (Gerstenberger et al., 2011a, b). The Z-factor is a parameter that describes the strength of shaking expected with an annual probability of exceedance of 1/500, and is used to scale the NZS1170 design spectra for the location of interest. The Department of Building and Housing (2011) promulgated the interim Z-factor of 0.3 in May, increased from the previous value of 0.22 for Christchurch, together with a modified 25-year R-factor for the serviceability limit state of 0.33, compared to the standard value of 0.25 in NZS1170. The revised values were to be applied within those parts of the regions of Christchurch City, Selwyn District and Waimakariri District where Z was previously less than 0.3. This paper summarises the justification of the preliminary updated Z-factor. It also discusses three sets of peak ground acceleration estimates that have been derived, for structural applications, for liquefaction assessments and for evaluating the probabilities of rock falls in the Port Hills.

Paper Number 115 1.1 Enhanced ground motions in the CBD in the February earthquake

Ground motions in the Christchurch CBD in the 22 February 2011 earthquake considerably exceeded the design levels for Christchurch specified in the New Zealand earthquake design standard NZS1170.5:2004. They were enhanced by factors of about 2 for the magnitude and distance of the earthquake from median values given by both the McVerry et al. (2006) New Zealand ground-motion prediction equation (GMPE) that was used in deriving the NZS1170 hazard spectra and in US GMPEs for the near-source distances relevant to the CBD. Figure 1 compares the NZS1170 deep soil spectra for Christchurch (hazard factor Z=0.22) with 5% damped acceleration response spectra of recorded motions in the magnitude 6.3 earthquake of 22 February 2011 at four sites within about 1.5 km of the Christchurch Central Business District. The thin lines are the larger value of the two horizontal components of the recorded motions. The solid red line is the geometric mean of these four larger horizontal component spectra. The dashed and solid black lines are the NZS1170 elastic spectra for return periods of 500 years (Return Period factor R=1.0) and 2500 years (R=1.8). Design spectra in NZS1170 are based on the larger horizontal component. The CBD spectra (coloured lines) are even higher than the 2500-year return ground motions, especially at long periods, although they are generally somewhat less than these motions at short periods (< 0.3 – 0.4 s). As for the 4 September 2010 earthquake, large amplitudes at long periods around 3s indicate that amplification effects due to the deep soils (> 500 m thick) below Christchurch are present. The maximum spectral displacement demands are associated with these peaks at 3.0-3.5s.

CENTRAL CITY AND NZS1170 SPECTRA CLASS D DEEP OR SOFT SOIL Larger Horizontal Components

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1.6 NZS1170 2500-yr Class D

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NZS1170 500-yr Class D Deep or Soft Soil 1.2

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GM_Larger_FEB 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Period T(s)

Figure 1 Comparison of recorded (5% damped) acceleration response spectra for four sites within ~1.5 km of the Christchurch CBD (coloured lines) and corresponding spectra from the New Zealand design standard NZS1170 for deep or soft soil sites (black lines). The solid red line is the geometric mean of the four central sites; dashed and solid black lines are the NZS1170 spectra for 500- and 2500-year return periods respectively. Figure 2 shows comparisons of the spectra of motions recorded at the four CBD sites with the 50- and 84-percentile spectra estimated using the McVerry et al. (2006) model for a magnitude 6.3 oblique- mechanism earthquake on Class D deep soil conditions at a closest distance of 4 km from the rupture, a representative distance for the CBD sites. The spectra of the recorded motions generally exceed the 84-percentile (one standard deviation above the median) motions for periods longer than about 0.35s. Figure 3 shows the larger horizontal component of the 5% damped response spectral accelerations of the recorded motions for 1s period with those estimated from the McVerry et al. model. The best-fit line shows that at near-source distances (within ~5 km of the fault, including central Christchurch)

2 spectral accelerations were considerably higher than those expected from the model for an earthquake of this magnitude. However, accelerations were somewhat less than expected at larger distances from the source (> 10 km). Similar behaviour was exhibited by the peak ground accelerations.

Figure 2 Comparison of spectra of recorded CBD motions with those predicted for Class D deep soil site conditions by the McVerry wet al. (2006) response spectrum model for a magnitude 6.3 oblique mechanism earthquake at 4 km distance from the rupture.

Figure 3 Recorded spectral accelerations at 1s period during the Christchurch earthquake and best fit curve independent of site classification (black line) compared to accelerations expected from the NZ national attenuation model (McVerry 2006) using a crustal oblique slip source. Segou & Kalkan (2011) reported overall good performance of five Next Generation Attenuation (NGA) models with respect to estimating the geometric means of the horizontal components in the Canterbury and Darfield earthquakes. However, careful inspection of the plots in the lower panels of their Figures 2 to 5 showed that the closest recorded motions in the Christchurch earthquake, corresponding to the sites around the CBD, were generally under-estimated by the models.

3 Some of the enhancement of motions over modelled values may be random variability, but much of it is likely to result from specific characteristics of the causative fault (Webb, 2011). These include high apparent stresses and rupture directivity of the earthquake (Fry and Gerstenberger, 2011). Some of these characteristics are likely to occur in future earthquakes in the region, increasing the ground- motions from those given by the GMPE used in the development of the NZS1170 spectra. The modelling performed to produce the new hazard estimates for Christchurch has accounted for the enhanced motions by applying the Atkinson & Boore (2006) multiplicative factors for stress-drop effects to the standard hazard estimates, and reducing the source depth to 5 km rather than the minimum of 10 km in the standard New Zealand National Seismic Hazard Model. The stress-drop term was a convenient readily available tool to produce enhanced motions, rather than representing a belief that high stress-drops were the only or major contributor to the strong motions. Other possible effects generally require complicated case-by-case modelling that could not have been achieved in the time-frame required for producing the interim design values for Christchurch.

1.2 Increased seismicity rates

Particularly challenging has been the need to take into account the time-varying nature of a productive on-going earthquake sequence around Christchurch. Seismicity in the region is presently very high relative to previous activity, but is likely to reduce with time, over a period of years to decades. This has been handled through combining time-independent and time-varying seismicity models (Figure 4), with earthquake forecasting models used for perhaps the first time to obtain hazard estimates for engineering design. Different time-scales have been of interest: months for decisions about re- occupation of properties threatened by rock fall, one or a few years for insurance purposes and for evaluating hazard during reconstruction, and 50 years for the nominal design lives of most structures.

Figure 4 Forecast annual earthquake rates for a representative Christchurch location from the three seismicity- based models for M5.0–5.9 (top), M6.0–M6.9 (middle) and M7.0–M7.9 (bottom). The dominance of the higher rates of the STEP model initially can be seen before the EEPAS model takes over at slightly longer time scales. After roughly 20 years, the time-invariant PPE smoothed seismicity model produces the highest rate.

4 The methodology combines hazard contributions from four earthquake source models as explained in detail in Gerstenberger et al. (2011a, b). The latest version of the National Seismic Hazard Model (NSHM), modified to use conditional probabilities for rupture of the major faults affecting the Christchurch region, is used to estimate the contributions from active faults. Three models are used in place of the distributed seismicity component of the NSHM. The contributions from aftershocks are accounted for with the Short Term Earthquake Probability (STEP) model (Gerstenberger et al., 2005). The Every Earthquake a Precursor According to Scale (EEPAS) model (Rhoades and Evison, 2004) accounts for mid-term modifications caused by earthquakes being precursors of later earthquakes. Longer-term seismicity is represented by the Proximity to Past Earthquakes (PPE) model (Rhoades and Evison, 2004), a spatially smoothed time-invariant model developed from past earthquake activity. It is similar to the background seismicity model used by the NSHM except that no catalogue declustering of events spaced closely in time and location (i.e. removal of aftershocks) is done prior to smoothing the earthquake data, and it includes the current earthquake sequence. Figure 4 shows the yearly forecasts for the three distributed source seismicity-based models for years 2011-2041. In this figure the sharp decay of the aftershock sequence from the STEP model is apparent as well as the slower temporal response of the EEPAS model and the static forecast of the PPE model. It can be seen that the STEP model is dominant initially in all magnitude ranges, with the dominance lasting longer for magnitudes 7.0-7.9. The EEPAS model then dominates the forecasts until roughly 2025 when the PPE model begins to produce the highest forecast rates. All these rates are considerably larger than those estimated before the start of the sequence.

2 HAZARD ESTIMATES

Revised earthquake ground-motion hazard estimates were obtained for the Christchurch region by implementing the seismicity model that combined time-varying and time-independent components. The seismicity associated with this model was all applied at a shallow depth of 5 km, rather than taking the shallowest seismicity layer at its usual depth of 10 km. Several other modifications were made to the usual modelling procedure, mainly in recognition of the very high seismicity rates that the model produced in the magnitude 5.0 to 5.5 range. The McVerry et al. model is known to increasingly over-estimate motions as the magnitude reduces below 5.5. In recognition of this spurious behaviour, and advice from the Engineering Advisory Group that earthquakes of magnitude less than 5.5 were unlikely to produce significant damage to code-designed structures, the minimum magnitude was increased from 5.0 to 5.5. Addition of a stress-drop term has been discussed above. The estimates for revised NZS1170 spectra for Christchurch were associated with the default design life of 50 years. The design life differs from the return periods associated with various limit states, which are the inverse of the annual exceedance probabilities (AEPs). For the time-independent hazard models that are usually used for deriving engineering design spectra, the seismicity rates are the same for every year, but for time-varying seismicity models they change from year-to-year. This was handled by calculating the expected number of earthquakes in magnitude bands of 0.2 width on a 0.1° by 0.1° grid for each year, and adding these over the 50-year duration of interest. This gave the effective seismicity rate over the 50-year design life for each grid cell and magnitude band, by dividing the total by 50. The resulting AEPs for various acceleration values were calculated using these effective seismicity rates. Calculations were also performed on a year-by-year basis, to track the change in ground motion level associated with a given annual exceedance rate.

2.1 Response spectra and Z-factors

Figure 5 shows the 5% damped elastic hazard spectrum for NZS1170 Class D Deep or Soft Soil that is estimated to have a 10% probability of exceedance in the next fifty years in the Christchurch CBD using the initial revised model, prior to the 13 June 2011 earthquake. This spectrum is compared with the NZS1170 Z=0.3 spectrum for this soil class, which is the basis for the recommendation of

5 increasing Z from 0.22 to 0.3. Beyond its short-period plateau, the Z=0.3 spectrum envelopes the 10% in 50 years spectrum. In general, the NZS1170 spectrum for a site usually envelopes its 10% in 50 year hazard spectrum, apart from truncating the peak of the spectrum by up to about 30%; the Z=0.3 spectrum in figure 5 is consistent with this requirement. It can be seen that the zero-period ordinate (i.e., peak ground acceleration) is 0.6g, considerably increased from the value of 0.34g that applies for the NZS1170 Class D spectrum for a Z-factor of 0.3.

NZS1170 Z=0.3 R=1.0 versus 10% in 50 years deep soil spectrum SA(T) (g) with stress drop factor for stress-drop ratio 1.5*standard

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0.8 NZS1170 Z=0.3 Class D 10% in 50 yrs Class D with stressdrop factor SA(T) (g) 0.6

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Figure 5 The Z=0.3 Class D deep soil spectrum approximately envelopes the hazard spectrum estimated with a 10% probability of exceedance in the next 50 years, apart from truncation of the peak of the spectrum.

In addition to the modified Z-factor, it was found that the rate of change of the spectra with AEP was different from that of NZS1170. In NZS1170, the return period factor for Serviceability Limit State 1 (SLS1) with an AEP of 1/25 is 0.25. For the new time-varying seismicity model, the SLS1 return period factor for Christchurch is 0.33.

2.2 Peak ground accelerations for structural and geotechnical applications

Geotechnical design is often based on peak ground acceleration values. As shown earlier, the peak ground accelerations calculated directly from the revised hazard model for Christchurch depart markedly from the values corresponding to a Z-factor of 0.3. Consequently, it was recommended that specific estimates of peak ground accelerations be used when they are required, rather than taking the values derived from the Ch(0)ZR product. Magnitude-weighting is an important issue for geotechnical design. Liquefaction and lateral spreading is strongly affected by duration, and its assessment frequently involves the use of magnitude- weighting factors (MWFs) in terms of magnitude M. The magnitude-weighting factors used for estimating the Z-factors were (M/7.5)1.285, as originally proposed by Idriss (1981) and used in the development of NZS1170.5. However, the MWFs used for liquefaction assessment have been re- evaluated in recent years (Youd & Idriss, 2001), and alternative MWFs of (M/7.5)2.5 have been used for estimating pgas for liquefaction assessment in Christchurch (Gerstenberger et al., 2011a). Conversely, for the assessment of rock fall, MWFs are not incorporated, because it is the exceedance of a critical acceleration for a single rather than multiple cycles that is important (Massey et al., 2011).

6 To satisfy these requirements, three sets of peak ground acceleration values have been derived directly from the hazard analyses. One set of peak ground acceleration values is relevant for structural applications and a second set for geotechnical evaluations of liquefaction-related issues (Gerstenberger et al., 2011a), each derived using the magnitude-weighting factors appropriate for their specific uses. Another set has been developed specifically for rock fall assessments on the Port Hills (Massey et al., 2011), accounting for the different site conditions there and omitting magnitude-weighting factors.

2.3 Motions for periods of 1.5s and longer

The evaluations to date do not consider the period range longer than 1.5s, for which the recorded motions in the September, February and June earthquakes show that the spectral shapes are enhanced from the NZS1170 Deep Soil shape between about 2s and 4s. The evaluation of the peaks in this period range, which provide the strongest spectral displacements in the recorded motions, is being undertaken in other studies using methods other than probabilistic seismic hazard analysis, such as SHAKE and 2- and 3-dimensional basin modelling, and possibly taking into account rupture- directivity effects. Evaluation of shear-wave travel times to the depth of the volc anic rocks underlying the CBD at about 550 m depth indicates that the long-period peaks occur in a period range similar to the site periods determined for one-dimensional site models. However, source effects of these earthquakes must also be important for the long-period response, as it is apparent in only some events, as discussed by Cousins et al. (2011) with respect to the September 2010 Darfield earthquake.

3 DISCUSSION

Considerable further hazard studies for Christchurch have occurred since the study presented here. The seismicity model was revised soon after the magnitude 6.0 earthquake of 13 June 2011, recognising the increased seismicity rates resulting from the resetting of the aftershock decay sequence by this event. That and other changes in the hazard estimation procedure have led to increased Z-factor estimates of 0.34-0.41, with Z=0.3 now found to correspond to the near-constant value that is achieved after about 15 years, as presented in the GNS evidence to the Royal Commission. More recently, an Expert Elicitation (EE) procedure has been undertaken, leading to recommendations for weighted combinations of multiple seismicity models for each of the aftershock, mid-term and long-term components of the model, as well as similar logic -tree approaches for other aspects of the hazard modelling (e.g. source depth, minimum magnitude, stress-drop modification and inclusion of epistemic variability in the GMPE). Also, Bradley & Cubrinovski (2011) have shown that a New Zealand–specific geometric -mean component model developed before the Canterbury earthquakes (Bradley, 2010) provided a good match for the Darfield and 22 February 2011 Christchurch earthquakes to the short-period motions (peak ground acceleration and 0.2s spectral acceleration) at all distances, and an under-prediction of 1.0s spectral accelerations only for a few sites at source-to-site distances less than 10km. The much improved performance of this model compared to that of McVerry et al. (2006) dictated that it should also be included as part of the revised hazard estimates. Revised seismicity rates from the EE model have recently been released, incorporating seismicity up to early January 2012. These were incorporated along with the other changes to hazard modelling, including addition of the Bradley GMPE, in late March 2012.

4 CONCLUSIONS

This paper summarises the background to the increase of the hazard factor Z for Christchurch in the New Zealand Standard NZS1170 Structural Design Actions from 0.22 to 0.30, for application to structures with fundamental periods up to 1.5s. Spectral accelerations for periods longer than 1.5s

7 should be derived from special studies. The return period factor R for Serviceability Limit State 1 associated with a return period of 25 years was increased from 0.25 to 0.33. Specific estimates of peak ground accelerations should be used when for structural and geotechnical assessments in Christchurch, rather than taking the values derived from the Ch(0)ZR product. Such estimates have been provided to DBH and are expected to be released in the near future, incorporating the modifications described in the Discussion section. A report describing the background to the hazard estimates for various purposes is in preparation.

REFERENCES

Atkinson, G. M. and D. M. Boore 2006. Earthquake ground-motion prediction equations for eastern North America, Bulletin of the Seismological Society of America, 96, 2181-2205. Bradley, B.A. 2010. NZ-specific pseudo-spectral acceleration ground motion prediction equations based on foreign models. Report No. 2010-03, Department of Civil and Natural Resources Engineering, University of Canterbury, Christchurch, New Zealand. Bradley, B.A. and Cubrinovski. M. 2011 Near-source strong ground motions observed in the 22 February 2011 Christchurch earthquake, Bulletin of the New Zealand Society for Earthquake Engineering, 44(4): 181-194. Department of Building and Housing 2011. Compliance Document for New Zealand Building Code. Clause B1. Structure. Amendment 10 (Canterbury). http://www.dbh.govt.nz/compliance-documents#B1 Fry, B. and Ge rstenberger, M.C. 2011 Large apparent stresses from the Canterbury earthquakes of 2010 and 2011. Seismological Research Letters, 82(6), 833-838. Gerstenberger, M., S. Wiemer, L.M. Jones, and P.A. Reasenberg 2005. Real-time forecasts of tomorrow’s earthquakes in California, Nature 435, 328-331. Gerstenberger, M.; Cubrinovski, M; McVerry, G.; Stirling, M.; Rhoades, D.; Bradley, B.; Langridge, R.; Webb, T.; Peng, B.; Pettinga, J.; Berryman, K.; Brackley, H. 2011. Probabilistic assessment of liquefaction potential for Christchurch in the next 50 years, GNS Science Report 2011/15 30 p. Gerstenberger, M.C.; McVerry, G.H.; Rhoades, D.A.; Stirling, M.W.; Berryman, K.; Webb, T. 2011. Update of the Z-factor for Christchurch considering earthquake clustering following the Darfield earthquake, GNS Science Report 2011/29 19 p. Idriss, I.M. 1985. Evaluating seismic risk in engineering practice. Proceedings of the 11th International Conference of Soil Mechanics and Foundation Engineering, Vol 1: 255-320. San Francisco. Massey, C., McSaveney, M., Buxton, R., Lukovic, B., Heron, D., Davies, T., Andres, N. 2011. Pilot study for assessing life-safety risk from rockfalls in the Port Hills, Christchurch, New Zealand. GNS Science Report 2011/16. McVerry, G.H., Zhao, J.X., Abrahamson, N.A. and Somerville, P.G. 2006. New Zealand acceleration response spectrum attenuation relations for crustal and subduction zone earthquakes. Bulletin of the New Zealand National Society for Earthquake Engineering, 39(1): 1-58. Rhoades, D.A.; Evison, F.F. 2004 Long-range earthquake forecasting with every earthquake a precursor according to scale. Pure and applied geophysics, 161(1): 47-72. Segou, M. and Kalkan, E. 2011 Ground motion attenuation during M7.1 Darfield and M6.2 Christchurch, New Zealand, earthquakes and performance of global predictive models. Seismological Research Letters, 82(6): 866-874. Standards New Zealand 2004. Structural design actions Part 5 Earthquake actions – New Zealand, New Zealand Standard NZS1170.5:2004. Webb, T.H. (compiler) 2011. The Canterbury earthquake sequence and implications for seismic design levels. GNS Science Consultancy Report 2011/183. 88p. Youd, T.L. and Idriss, I.M. 2001 Liquefaction resistance of soils: summary report from the 1996 NCEER and 1998 NCEER/NSF Workshops on evaluation of liquefaction resistance of soils. ASCE Journal of Geotechnical and Geoenvironmental Engineering, 127(4), 297-313.

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